Using the bar model to ease the transition from transforming arithmetic-numerical to algebraic equations: theoretical considerations and possible obstacles

Anna-Katharina Roos (1) , Leander Kempen (1)

1 TU Dortmund University, Germany

We discuss an approach to transforming and solving algebraic equations via the so-called bar model, based on the strategy of transposing. After developing a learning environment, we conducted design experiments to get insights into how students work with it. First, this paper aims to present the core idea of our learning environment. Second, we highlight the following difficulties that students face when working with the bar model: (1) the model itself, with its translation processes between graphical and symbolic representations (such as numbers, variables or operation signs), turned out to be a considerable learning content, (2) the transition from arithmetic-numerical contexts to general algebraic equations in the bar model seems to bear distinct conceptual obstacles which may even lead to misconceptions based on over-generalizations resulting from the bar model. We point to theoretical insights and implications for enhancing our learning environment.

Mots clés: Bar model; equations; algebra; design research

Domaines: Mathématiques [math]

Anna-Katharina Roos, Leander Kempen. Using the bar model to ease the transition from transforming arithmetic-numerical to algebraic equations: theoretical considerations and possible obstacles. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12), Feb 2022, Bozen-Bolzano, Italy. ⟨hal-03745423⟩